Boosting the Electrocatalytic Oxygen Reduction Activity of MnN4-Doped Graphene by Axial Halogen Ligand Modification

Exploring highly active electrocatalysts as platinum (Pt) substitutes for the oxygen reduction reaction (ORR) remains a significant challenge. In this work, single Mn embedded nitrogen-doped graphene (MnN4) with and without halogen ligands (F, Cl, Br, and I) modifying were systematically investigated by density functional theory (DFT) calculations. The calculated results indicated that these ligands can transform the dyz and dxz orbitals of Mn atom in MnN4 near the Fermi-level into dz2 orbital, and shift the d-band center away from the Fermi-level to reduce the adsorption capacity for reaction intermediates, thus enhancing the ORR catalytic activity of MnN4. Notably, Br and I modified MnN4 respectively with the lowest overpotentials of 0.41 and 0.39 V, possess superior ORR catalytic activity. This work is helpful for comprehensively understanding the ligand modification mechanism of single-atom catalysts and develops highly active ORR electrocatalysts.


Introduction
With the ever-increasing energy crisis and environmental issues, a major challenge facing mankind is to develop eco-friendly and renewable energy conversion and storage devices, such as fuel cells and rechargeable batteries [1][2][3].However, due to the sluggish kinetics of the cathodic oxygen reduction reaction (ORR), these devices are heavily dependent on Pt catalysts to accelerate the reaction process [4,5].Unfortunately, the natural scarcity and prohibitive cost of Pt greatly increased the large-scale commercialization cost of fuel cells and rechargeable batteries [6,7].Therefore, it is imperative to explore inexpensive and high-performance materials as alternatives to Pt catalysts.
In this case, graphene-supported nitrogen-doped transition metal (M−N−G) single atom catalysts (SACs) have attracted increasing attention because of their efficient use of atoms and their outstanding mechanical flexibility, and which are considered as promising alternative material to Pt catalysts [8][9][10].However, their catalytic activities are greatly impeded by the unsatisfactory adsorption strength for ORR intermediates [11,12].Optimizing the electronic structure of metal active center can further improve their catalytic activities, including axial ligand coordination engineering, heteroatom doping, and the construction of diatomic or polyatomic active sites [13][14][15].Among which, axial ligand coordination engineering was proved to be a novel and feasible strategy to boost the catalytic activity of M−N−Gs, especially for halogen ligands [13,[16][17][18][19][20][21].For example, Han et.al.successfully prepared an FeN 4 Cl catalyst with a half-wave potential of 0.921 V, which showed remarkably enhanced ORR catalytic activity compared to FeN 4 .Furthermore, density functional theory (DFT) calculations indicated that the axial Cl ligand can effectively modulate the adsorption capacity of FeN 4 for reaction intermediates and transform the rate-determination step (RDS) of *OH reduction into *OOH formation, resulting in the superior ORR activity of FeN 4 Cl [22].Both experiments and DFT calculations have confirmed that FeN 4 I possesses superior ORR catalytic activity, and the corresponding half-wave potential can reach to 0.948 V, which should be attributed to the appearance of Fe d z 2 orbital with a lower energy level caused by I modification [23].Chen et al. studied a series of MN 4 X (M = Fe, Co, and Ni; X = F, Cl, Br, and I) catalysts by performing DFT calculations, and found that axial coordination of X can modulate the electronic structure of M active center to alter the binding of MN 4 with reaction intermediates.In particular, CoN 4 Cl and CoN 4 Br, respectively, with ultralow overpotentials of 0.25 and 0.26 V possess excellent ORR catalytic activity [24].In addition, the axial halogen ligand can regulate the selectivity of the ORR pathway.For example, different from the four-electron (4e − ) ORR pathway on CuN 4 and ZnN 4 , CuN 4 Cl and ZnN 4 Br are more favorable with a two-electron (2e − ) ORR pathway to form H 2 O 2 , and the overpotentials are only 0.07 and 0.05 V, respectively [25].Although certain M−N−Gs modified by halogen ligands have shown excellent catalytic activity, a comprehensive examination of single Mn−embedded and N−doped graphene (MnN 4 ) modified by various halogen ligands (F, Cl, Br, and I) is still lacking.According to available studies, the overpotential of ORR on MnN 4 is about 0.90 V [26], which is significantly higher than those for Pt (100) (0.47 V) [27] and Pt (111) (0.44 V) [28].Therefore, it is expected to reduce the ORR overpotential and enhance the catalytic activity of MnN 4 by halogen ligand modification.Moreover, how the halogen ligands regulate the electronic structures, reaction intermediates adsorption characteristics, ORR catalytic activity, and reaction mechanism of MnN 4 remain to be further explored.
Herein, halogen ligands X (X = F, Cl, Br, and I) were introduced to axially modify the active center of MnN 4 , named MnN 4 −X.The structural stabilities, electronic properties, and catalytic characters of MnN 4 and MnN 4 −X were investigated by DFT calculations.Our calculated results showed that axial halogen ligands can significantly improve the ORR activity of MnN 4 .In particular, the overpotentials of MnN 4 −Cl, MnN 4 −Br, and MnN 4 −I are 0.44, 0.41, and 0.39 V, respectively, which are comparable to or even better than those of Pt catalysts.This work provides great significance for the design and development of low cost and high efficiency graphene-based electrocatalysts.

Structural Model
A 5 × 5 graphene supercell containing 50 carbon atoms was used to construct a MnN 4 catalyst, as shown in Figure 1.It can be seen that all of the atoms are kept in the same plane, and the average bond length of Mn−N bonds, the formation energy (E f1 ), and the binding energy between Mn and N 4 −G (E b1 ) are 1.916 Å, −3.16 eV, and 6.90 eV, respectively.These values are consistent with those (1.920Å, −3.07 eV, and 6.84 eV) in available studies [26,29,30], implying the reliability of our calculations.Moreover, the negative E f1 and the E b1 larger than the cohesive energy (3.87 eV) of bulk Mn indicate the good structural stability of MnN 4 .Hence, both sides of MnN 4 can adsorb ORR intermediates, potentially realizing an axial ligand coordination with the Mn atom [8,31].Thus, axial halogen ligand X was introduced into MnN 4 to form MnN 4 −X catalysts (see Figure 1).Due to the effect of X, the average bond lengths of Mn−N bonds in MnN 4 −F, MnN 4 −Cl, MnN 4 −Br, and MnN 4 −I are, respectively, stretched into 1.975 Å, 1.975 Å, 1.973 Å, and 1.971 Å.Meanwhile, the Mn atom is deviated from the plane of graphene.To evaluate the structural stabilities MnN 4 −X, the binding energies (E b2 ) between X and MnN 4 and the formation energy (E f2 ) for MnN 4 −X were calculated by Equations (10) and (12) and are presented in Figure 2. One can find that all MnN 4 −X structures have smaller formation energy than that of MnN 4 , indicating the better structural stability of MnN 4 −X than MnN 4 .Moreover, the positive values of E b2 suggest the good combinations between X and MnN 4 .Furthermore, the AIMD simulations show that the energy of each MnN 4 and MnN 4 −X structure smoothly oscillates around a certain value, and there is no bond breakage, although their structures were wrinkled to some extent, as indicated by Figure S1.These results indicate that all structures mentioned above are thermodynamically stable.In addition, according to the calculated positive values of U diss in Table S1, all structures are verified to be electrochemically stable.Therefore, all MnN 4 and MnN 4 −X structures are thermodynamically and electrochemically stable and are considered in the following discussions.From the Bader charge analyses in Table S1, the Mn atom loses 1.28 e − to N 4 −G in MnN 4 .After introducing X into MnN 4 , the ligands of F, Cl, Br, and I, respectively, obtained 0.65, 0.59, 0.53, and 0.47 e − from the Mn atom, in agreement with the electronegative order of F (3. structures mentioned above are thermodynamically stable.In addition, according to the calculated positive values of Udiss in Table S1, all structures are verified to be electrochemically stable.Therefore, all MnN4 and MnN4−X structures are thermodynamically and electrochemically stable and are considered in the following discussions.From the Bader charge analyses in Table S1, the Mn atom loses 1.28 e − to N4−G in MnN4.After introducing X into MnN4, the ligands of F, Cl, Br, and I, respectively, obtained 0.65, 0.59, 0.53, and 0.47 e − from the Mn atom, in agreement with the electronegative order of F (3.98) > Cl (3.16) > Br (2.96) > I (2.66).The Mn atom loses more charges than that in MnN4, presenting the order of MnN4−F (1.50 e) > MnN4−Cl (1.40 e) > MnN4−Br (1.36 e) > MnN4−I (1.30 e).Therefore, the X ligand modification would lead to different charge densities of Mn atoms and affect the adsorption activities for ORR intermediates.structures mentioned above are thermodynamically stable.In addition, according to the calculated positive values of Udiss in Table S1, all structures are verified to be electrochemically stable.Therefore, all MnN4 and MnN4−X structures are thermodynamically and electrochemically stable and are considered in the following discussions.From the Bader charge analyses in Table S1, the Mn atom loses 1.28 e − to N4−G in MnN4.After introducing X into MnN4, the ligands of F, Cl, Br, and I, respectively, obtained 0.65, 0.59, 0.53, and 0.47 e − from the Mn atom, in agreement with the electronegative order of F (3.98) > Cl (3.16) > Br (2.96) > I (2.66).The Mn atom loses more charges than that in MnN4, presenting the order of MnN4−F (1.50 e) > MnN4−Cl (1.40 e) > MnN4−Br (1.36 e) > MnN4−I (1.30 e).Therefore, the X ligand modification would lead to different charge densities of Mn atoms and affect the adsorption activities for ORR intermediates.

Adsorption of Intermediates
According to the Sabatier's principle [32], the catalytic activity of catalysts is strongly dependent on the adsorption strength for reaction intermediates.Thus, the adsorption characteristics of ORR intermediates on MnN 4 and MnN 4 −X were explored.After optimizing all horizontal and vertical configurations of *O 2 , *OOH, *O, and *OH with different orientations on all catalysts, the most stable adsorption structures were obtained and are presented in Figure 3.It can be seen from this figure that all intermediates are preferably adsorbed on the Mn site through an O atom, indicating that the Mn atom is the active center in MnN 4 and MnN 4 −X.This is understandable since the net spin charges mainly distribute on the Mn atom in MnN 4 and MnN 4 −X (see Figure 4).In theory, the adsorption of the O 2 molecule is regarded as a prerequisite for triggering the ORR, so it is firstly considered.As shown in Figure 3 S2), and MnN 4 exhibits the strongest adsorption capability to O 2 .Among this, the adsorption energy of O 2 on MnN 4 is in agreement with the values of −1.33 and −1.43 eV in previous studies [9,26,29].Meanwhile, the O−O bonds are, respectively, elongated from 1.232 Å in gas-phase O 2 to 1.392, 1.302, 1.305, 1.304, and 1.295 Å.Since the spin charges of the active center and the Bader charges analysis can be used to describe the binding strength between the metal center and adsorbate in the catalysts [33][34][35], the spin charges of the Mn atom and the charges transfer between O 2 and the catalysts were calculated to explore the difference of O 2 adsorption strength on MnN 4 and MnN 4 −X. Figure 4 and Table S3 show that the spin charge of the Mn atom in MnN 4 is significantly higher than that in MnN 4 −X, and the Mn atom in MnN 4 can transfer more charges (0.  S2.Therefore, the X ligand modification can effectively alter the adsorption capacity of MnN 4 towards reaction intermediates, and then optimize the ORR catalytic activity.

Adsorption of Intermediates
According to the Sabatier's principle [32], the catalytic activity of catalysts is strongly dependent on the adsorption strength for reaction intermediates.Thus, the adsorption characteristics of ORR intermediates on MnN4 and MnN4−X were explored.After optimizing all horizontal and vertical configurations of *O2, *OOH, *O, and *OH with different orientations on all catalysts, the most stable adsorption structures were obtained and are presented in Figure 3.It can be seen from this figure that all intermediates are preferably adsorbed on the Mn site through an O atom, indicating that the Mn atom is the active center in MnN4 and MnN4−X.This is understandable since the net spin charges mainly distribute on the Mn atom in MnN4 and MnN4−X (see Figure 4).In theory, the adsorption of the O2 molecule is regarded as a prerequisite for triggering the ORR, so it is firstly considered.As shown in Figure 3, the O2 molecule tends to adsorb on the Mn site through side-on configuration in MnN4 but through end-on configuration in MnN4−X.The adsorption energies of O2 on MnN4, MnN4−F MnN4−Cl, MnN4−Br, and MnN4−I, respectively, are −1.34,−0.51, −0.25, −0.26, and −0.44 eV (see Table S2), and MnN4 exhibits the strongest adsorption capability to O2.Among this, the adsorption energy of O2 on MnN4 is in agreement with the values of −1.33 and −1.43 eV in previous studies [9,26,29].Meanwhile, the O−O bonds are, respectively, elongated from 1.232 Å in gas-phase O2 to 1.392, 1.302, 1.305, 1.304, and 1.295 Å.Since the spin charges of the active center and the Bader charges analysis can be used to describe the binding strength between the metal center and adsorbate in the catalysts [33][34][35], the spin charges of the Mn atom and the charges transfer between O2 and the catalysts were calculated to explore the difference of O2 adsorption strength on MnN4 and MnN4−X.Figure 4 and Table S3 show that the spin charge of the Mn atom in MnN4 is significantly higher than that in MnN4−X, and the Mn atom in MnN4 can transfer more charges (0.70 e − ) to O2 than that in MnN4−X (0.50, 0.53, 0.51, and 0.44 e − , respectively, for MnN4−F, MnN4−Cl, MnN4−Br, and MnN4−I), indicating the strongest interactions between O2 and MnN4.However, the adsorption energy of MnN4 for O2 is much stronger than that on Pt (−1.10 eV) [27], FeN4 (−1.13 eV), and CoN4 (−0.90 eV) [36], which may hinder the subsequent reaction processes.In contrast, MnN4−X is likely to possess better ORR activity than Pt, FeN4, CoN4, and MnN4.Similar to the adsorption of the O2 molecule, the X ligand can weaken the interactions between *OOH, *O, and *OH and MnN4 to different extents, as shown in Table S2.Therefore, the X ligand modification can effectively alter the adsorption capacity of MnN4 towards reaction intermediates, and then optimize the ORR catalytic activity.

Catalytic Performance
According to the 4e − reaction pathway (Equations ( 1)-( 4)) of ORR, the free energy change for all catalysts was calculated by Equation ( 7) and presented in Table S2 and Figure 5 to evaluate the catalytic performance.At zero electrode potential, the free energy in the whole reaction progress is gradually decreased for all catalysts, which means that each step of the reaction is exothermic and can spontaneously proceed.When increasing electrode potential, MnN4, MnN4−F, MnN4−Cl, MnN4−Br, and MnN4−I, respectively, present working potentials of 0.34, 0.59, 0.79, 0.82, and 0.84 V for maintaining the exothermic reaction process (see Figure 5).Among this, MnN4−Br and MnN4−I with larger working potentials are more prone to promote ORR compared with other catalysts.Under the standard ORR potential of 1.23 V, some reaction steps become uphill and are thermodynamically unfavorable.In particular, the hydrogenation of *OH to H2O with the maximum free energy barrier is the RDS for the ORR on all catalysts.In order to intuitively compare the catalytic activity, the theoretical overpotential is calculated through Equation ( 8) and illustrated in Figure 5.Note that the lower overpotential represents the higher ORR activity.The overpotentials of MnN4, MnN4−F, MnN4−Cl, MnN4−Br, and MnN4−I are 0.89, 0.64, 0.44, 0.41, and 0.39 V, respectively.Evidently, MnN4−I with the lowest overpotential of 0.39 V exhibits the best catalytic activity.Compared with the overpotentials of Pt (100) (0.47 V) [27] and Pt (111) (0.43 V) [28], MnN4−Cl and MnN4−Br/I, respectively, show comparable and higher catalytic activity, indicating that MnN4−Cl, MnN4−Br, and MnN4−I should be promising alternatives to Pt catalysts.Thus, X ligand modification is an effective strategy to improve the ORR catalytic activity of MnN4.Besides the 4e − reaction pathway, the 2e − reaction pathway (Equations ( 5) and ( 6)) [37,38] is also investigated to identify the ORR selectivity of all catalysts.The optimized adsorption structures of H2O2 on MnN4 and MnN4−X in Figure S2

Catalytic Performance
According to the 4e − reaction pathway (Equations ( 1)-( 4)) of ORR, the free energy change for all catalysts was calculated by Equation ( 7) and presented in Table S2 and Figure 5 to evaluate the catalytic performance.At zero electrode potential, the free energy in the whole reaction progress is gradually decreased for all catalysts, which means that each step of the reaction is exothermic and can spontaneously proceed.When increasing electrode potential, MnN 4 , MnN 4 −F, MnN 4 −Cl, MnN 4 −Br, and MnN 4 −I, respectively, present working potentials of 0.34, 0.59, 0.79, 0.82, and 0.84 V for maintaining the exothermic reaction process (see Figure 5).Among this, MnN 4 −Br and MnN 4 −I with larger working potentials are more prone to promote ORR compared with other catalysts.Under the standard ORR potential of 1.23 V, some reaction steps become uphill and are thermodynamically unfavorable.In particular, the hydrogenation of *OH to H 2 O with the maximum free energy barrier is the RDS for the ORR on all catalysts.In order to intuitively compare the catalytic activity, the theoretical overpotential is calculated through Equation ( 8) and illustrated in Figure 5.Note that the lower overpotential represents the higher ORR activity.The overpotentials of MnN 4 , MnN 4 −F, MnN 4 −Cl, MnN 4 −Br, and MnN 4 −I are 0.89, 0.64, 0.44, 0.41, and 0.39 V, respectively.Evidently, MnN 4 −I with the lowest overpotential of 0.39 V exhibits the best catalytic activity.Compared with the overpotentials of Pt (100) (0.47 V) [27] and Pt (111) (0.43 V) [28], MnN 4 −Cl and MnN 4 −Br/I, respectively, show comparable and higher catalytic activity, indicating that MnN 4 −Cl, MnN 4 −Br, and MnN 4 −I should be promising alternatives to Pt catalysts.Thus, X ligand modification is an effective strategy to improve the ORR catalytic activity of MnN 4 .Besides the 4e − reaction pathway, the 2e − reaction pathway (Equations ( 5) and ( 6)) [37,38]

Origin of the Catalytic Activity
To specifically analyze the origin of excellent catalytic activity of MnN4−X, the projected density of states (PDOS), d-band center, and the local density of states (LDOS) of Mn in MnN4 and MnN4−X were presented in Figure 6.It can be seen from this figure that that the dyz and dxz orbitals of Mn atoms in MnN4 are mainly located near the Fermi-level.When incorporating X ligand into MnN4, the d-orbital of the Mn atom moves towards the Fermilevel, and the main contribution near the Fermi-level is transformed into the d z 2 orbital, resulting in the enhanced reaction activity.Therefore, the O2 adsorption configuration is transformed from side-on for MnN4 into end-on for MnN4−X.Moreover, the d z 2 orbital occupations near the Fermi-level are significantly weaker than dyz and dxz orbitals in MnN4, and the d-band center of the Mn atom in MnN4 downshift from −0.81 eV to −1.10, −1.13, −1.11, and −1.07 eV in MnN4−F, MnN4−Cl, MnN4−Br, and MnN4−I, respectively.These changes result in the weakened adsorption capacity of MnN4−X for reaction intermediates as compared with MnN4.In particular, MnN4−Cl, MnN4−Br, and MnN4−I present appropriate adsorption strength for reaction intermediates and excellent ORR catalytic activity.In addition, the electronic band structures play an important role in determining the electronic transmission properties of catalysts [39].Hence, we further examine the total density of states (TDOS) of MnN4 and MnN4−X.As shown in Figure S3, after modifying with X, both spin-up and spindown orbitals of MnN4 cross through the Fermi-level, achieving the transition from semiconductor to metallic behaviors.This is conducive to the electron transfer during the reaction process, thereby enhancing the ORR catalytic activity.Therefore, halogen ligand modification can be an effective strategy to regulate the electronic structure of metal active center and improve the ORR catalytic activity of graphene-based SACs.In addition, the electronic band structures play an important role in determining the electronic transmission properties of catalysts [39].Hence, we further examine the total density of states (TDOS) of MnN 4 and MnN 4 −X.As shown in Figure S3, after modifying with X, both spin-up and spin-down orbitals of MnN 4 cross through the Fermi-level, achieving the transition from semiconductor to metallic behaviors.This is conducive to the electron transfer during the reaction process, thereby enhancing the ORR catalytic activity.Therefore, halogen ligand modification can be an effective strategy to regulate the electronic structure of metal active center and improve the ORR catalytic activity of graphene-based SACs.

Computational Method
All spin-polarized DFT calculations were performed using the Vienna ab initio Simulation Package (VASP) [40].The Perdew-Burke-Ernzerhof (PBE) within the generalized gradient approximate functional (GGA) was used to deal with exchange-correlation interactions [40,41].For all calculations, the kinetic energy cutoff was chosen to be 500 eV, thus achieving good energy convergence.The thickness of the vacuum layer was set to be 15 Å to avoid interactions between mirror images.All structures were allowed to converge until Feynman Hallman forces were smaller than 0.02 eV/Å, and the total energy fluctuation was set to be 10 −5 eV.The Brillouin zone was sampled with 5 × 5 × 1 k-points for structural optimization, and 11 × 11 × 1 k-points were sampled for the electronic structure calculations.The DFT-D3 method with the Becke-Johnson damping function was used to correct the van der Waals force dispersion [42].Ab initio molecular dynamics (AIMD) simulations were performed using the Nosé-Hoover thermostat at 300 K in the canonical ensemble (NVT) with a time step of 1 fs and a total time scale of 10 ps.
ORR includes two different competing reaction pathways, namely, the 4e − reaction pathway for the reduction of O2 to H2O and the 2e -reaction pathway for the reduction of O2 to H2O2.The 4e − reaction process under an acidic medium is listed as follows *O + H + + e -= *OH The 2e -reaction process under an acidic medium is presented as follows * + O 2 + H + + e -= *OOH (5)

Computational Method
All spin-polarized DFT calculations were performed using the Vienna ab initio Simulation Package (VASP) [40].The Perdew-Burke-Ernzerhof (PBE) within the generalized gradient approximate functional (GGA) was used to deal with exchange-correlation interactions [40,41].For all calculations, the kinetic energy cutoff was chosen to be 500 eV, thus achieving good energy convergence.The thickness of the vacuum layer was set to be 15 Å to avoid interactions between mirror images.All structures were allowed to converge until Feynman Hallman forces were smaller than 0.02 eV/Å, and the total energy fluctuation was set to be 10 −5 eV.The Brillouin zone was sampled with 5 × 5 × 1 k-points for structural optimization, and 11 × 11 × 1 k-points were sampled for the electronic structure calculations.The DFT-D3 method with the Becke-Johnson damping function was used to correct the van der Waals force dispersion [42].Ab initio molecular dynamics (AIMD) simulations were performed using the Nosé-Hoover thermostat at 300 K in the canonical ensemble (NVT) with a time step of 1 fs and a total time scale of 10 ps.
ORR includes two different competing reaction pathways, namely, the 4e − reaction pathway for the reduction of O 2 to H 2 O and the 2e − reaction pathway for the reduction of O 2 to H 2 O 2 .The 4e − reaction process under an acidic medium is listed as follows The change in Gibbs free energy for each step of the reaction is defined as (7) where ∆E DFT represents the total energy calculated by DFT.∆E ZPE and ∆S, respectively, are the changes in zero-point energy and entropy.T stands for the room temperature of 298.15 K. ∆G U = −neU, where n is the number of electrons required to complete the reaction, and U is the electrode potential.∆G PH = k B T × ln10 × pH, in which k B stands for the Boltzmann's constant, and pH is set to 0 in an acidic medium.
For the 4e − reaction pathway, the step with the maximum free energy barrier is considered to be the RDS.The overpotential of the whole reaction progress is calculated by the following equation The binding energy (E b1 ) between Mn and N−coordinated graphene (N 4 −G) and the binding energy (E b2 ) between MnN 4 and X are, respectively, given by the following equations (9) where E Mn , E N 4 −G , E MnN 4 , and E MnN 4 −X represent the total energies of a single Mn atom, N 4 −G, MnN 4 , and X modified MnN 4 , respectively.E X 2 represents the energy of a single halogen molecule.The formation energies (E f1 and E f2 ) of MnN 4 and MnN 4 −X are, respectively, de- fined as where µ C , µ N , and µ X denote the chemical potentials of C, N, and halogen atoms, which can be obtained from perfect graphene, nitrogen gas, and halogen molecules, respectively.The adsorption energy (E ads ) of catalysts for reaction intermediates is defined as the following equation E ads = E sup+inter − E sup − E inter (13) where E sup+inter , E sup , and E inter represent the energies of the adsorption system, the individual support, and the reaction intermediates, respectively.In addition, the electrochemical stability of catalysts can be evaluated by the solution potential (U diss ) [43], which is defined as where U • diss (metal, bulk) and n represent the standard dissolution potential of bulk metal and the number of electrons involved in the dissolution, respectively.U diss > 0 vs. the standard hydrogen electrode means that the system is electrochemically stable.

Conclusions
In summary, the structural stabilities, electronic structures, and ORR catalytic performances of MnN 4 with and without halogen ligand X (X = F, Cl, Br, and I) modification were systemically investigated by DFT calculations.The calculated results show that the MnN 4 and MnN 4 −X catalysts are thermodynamically and electrochemically stable, and follow the four-electron ORR pathway.After introducing axial X into MnN 4 , the X can obtain some electrons from the Mn atom in MnN 4 and regulate the electronic structures of the Mn atom.The d yz and d xz orbitals of the Mn atom near the Fermi-level are transformed into the weaker d z 2 orbital, and the d-band center of the Mn atom is shifted away from the Fermi-level, resulting in the reduced adsorption strength of MnN 4 for *OH.Thus, all MnN 4 −X catalysts present enhanced ORR catalytic activity compared with MnN 4 .In particular, MnN 4 −Br and MnN 4 −I exhibit excellent ORR catalytic activity, respectively, with the overpotentials of 0.41 and 0.39 V, which are superior to MnN 4 and Pt catalysts.Halogen ligand modification was identified to be an effective strategy for improving the ORR catalytic activity.This study is expected to provide a new perspective for the design and development of highly active graphene-based single-atom ORR catalysts.

Figure 1 .
Figure 1.Schematic diagram of MnN4 and MnN4−X structures.Grey, blue, green, and purple balls represent C, N, Mn, and X (X = F, Cl, Br, and I) atoms, respectively.

Figure 2 .
Figure 2. The binding and formation energies for MnN4 and MnN4−X.

Figure 1 .
Figure 1.Schematic diagram of MnN 4 and MnN 4 −X structures.Grey, blue, green, and purple balls represent C, N, Mn, and X (X = F, Cl, Br, and I) atoms, respectively.

Figure 1 .
Figure 1.Schematic diagram of MnN4 and MnN4−X structures.Grey, blue, green, and purple balls represent C, N, Mn, and X (X = F, Cl, Br, and I) atoms, respectively.

Figure 2 .
Figure 2. The binding and formation energies for MnN4 and MnN4−X.Figure 2. The binding and formation energies for MnN 4 and MnN 4 −X.

Figure 2 .
Figure 2. The binding and formation energies for MnN4 and MnN4−X.Figure 2. The binding and formation energies for MnN 4 and MnN 4 −X.

Figure 3 .
Figure 3. Schematic diagram of the most stable adsorption structures of intermediates on MnN4 and MnN4−X.Grey, blue, green, purple, red, and yellow balls represent C, N, Mn, X, O, and H atoms, respectively."*" indicates the clean surface.

Figure 3 .
Figure 3. Schematic diagram of the most stable adsorption structures of intermediates on MnN 4 and MnN 4 −X.Grey, blue, green, purple, red, and yellow balls represent C, N, Mn, X, O, and H atoms, respectively."*" indicates the clean surface.

Figure 4 .
Figure 4. Spin-resolved charge densities of Mn atom in MnN4 and MnN4−X with an isosurface value of 0.06 e/Å 3 .Green and blue balls represent Mn and N atom, respectively.
indicate that the H2O2 molecules cannot be stably adsorbed on MnN4, MnN4−Cl, and MnN4−Br and decompose into *O and H2O, which is consistent with the hydrogenation products of *OOH in the 4e − reaction pathway, implying the better 4e − reaction pathway selectivity.Although MnN4−F and MnN4−I can physically adsorb H2O2 with the adsorption energies of −0.08 and −0.06 eV, the free energy changes of *OOH to *O+H2O at zero electrode potential for MnN4−F (−1.70 eV) and MnN4−I (−1.86 eV) are significantly smaller than that (−0.20 and −0.39 eV) for *OOH to H2O2, indicating the 4e − reaction pathway is easier to occur.Therefore, the ORR tends to follow the 4e − reaction pathway on all catalysts.

Figure 4 .
Figure 4. Spin-resolved charge densities of Mn atom in MnN 4 and MnN 4 −X with an isosurface value of 0.06 e/Å 3 .Green and blue balls represent Mn and N atom, respectively.
is also investigated to identify the ORR selectivity of all catalysts.The optimized adsorption structures of H 2 O 2 on MnN 4 and MnN 4 −X in Figure S2 indicate that the H 2 O 2 molecules cannot be stably adsorbed on MnN 4 , MnN 4 −Cl, and MnN 4 −Br and decompose into *O and H 2 O, which is consistent with the hydrogenation products of *OOH in the 4e − reaction pathway, implying the better 4e − reaction pathway selectivity.Although MnN 4 −F and MnN 4 −I can physically adsorb H 2 O 2 with the adsorption energies of −0.08 and −0.06 eV, the free energy changes of *OOH to *O+H 2 O at zero electrode potential for MnN 4 −F (−1.70 eV) and MnN 4 −I (−1.86 eV) are significantly smaller than that (−0.20 and −0.39 eV) for *OOH to H 2 O 2 , indicating the 4e − reaction pathway is easier to occur.Therefore, the ORR tends to follow the 4e − reaction pathway on all catalysts.

Figure 5 .
Figure 5. Free-energy diagrams and overpotentials of ORR on all catalysts."*" indicates the clean surface.

Figure 5 .
Figure 5. Free-energy diagrams and overpotentials of ORR on all catalysts."*" indicates the clean surface.

2. 4 .
Origin of the Catalytic Activity To specifically analyze the origin of excellent catalytic activity of MnN 4 −X, the pro- jected density of states (PDOS), d-band center, and the local density of states (LDOS) of Mn in MnN 4 and MnN 4 −X were presented in Figure 6.It can be seen from this figure that that the d yz and d xz orbitals of Mn atoms in MnN 4 are mainly located near the Fermi-level.When incorporating X ligand into MnN 4 , the d-orbital of the Mn atom moves towards the Fermi-level, and the main contribution near the Fermi-level is transformed into the d z 2 orbital, resulting in the enhanced reaction activity.Therefore, the O 2 adsorption configuration is transformed from side-on for MnN 4 into end-on for MnN 4 −X.Moreover, the d z 2 orbital occupations near the Fermi-level are significantly weaker than d yz and d xz orbitals in MnN 4 , and the d-band center of the Mn atom in MnN 4 downshift from −0.81 eV to −1.10, −1.13, −1.11, and −1.07 eV in MnN 4 −F, MnN 4 −Cl, MnN 4 −Br, and MnN 4 −I, respectively.These changes result in the weakened adsorption capacity of MnN 4 −X for reaction intermediates as compared with MnN 4 .In particular, MnN 4 −Cl, MnN 4 −Br, and MnN 4 −I present appropriate adsorption strength for reaction intermediates and excellent ORR catalytic activity.

Figure 6 .
Figure 6.The PDOS and the LDOS within the range of −0.6 to 0 eV for Mn in MnN4 and MnN4−X.

Figure 6 .
Figure 6.The PDOS and the LDOS within the range of −0.6 to 0 eV for Mn in MnN 4 and MnN 4 −X.